LONDON—Barclays PLC plans to sell or exit most of its commodities businesses as part of an effort to shrink its investment bank and improve returns.

The U.K. bank will pull back from trading in base metals, energy and agricultural products and fold its precious-metals business into its currency-trading unit, people familiar with the plans said Monday. The move comes as Barclays prepares to tell investors on May 8 how it will reshape...